I have been asked to report on the relationship between two right-skew financial variables using R-squared e.g. "market cap explain ?% of the variance in CEO compensation". The purpose of the reporting is to help non-technical people understand the industry environment.

It makes sense to look at the relationships after applying a log transform to both variables. (Dampening the effect of the extreme positive values makes the relationships become much more linear, the residuals become approximately normal etc.)

However, the audience I am reporting the results to will not understand the sentence "log market cap explains ?% of the variance in log CEO compensation". They don't understand the idea of a logarithm or data transformations. Any ideas on saying the exact same thing in an accessible way?

Note: I am not resorting to discussing individual regression coefficients because I am also reporting on R-squared for multivariate models and have been asked to talk about the variance explained by 2+ variables together.

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    $\begingroup$ You don't say what your audience will understand, but more people know that it is often a good idea to talk of percent change, meaning that change is assessed multiplicatively, than consciously know or remember logarithms. That may be a hint of what logarithms are all about. Why not show the graph with CEO compensation and market cap and discuss the uncertainty in terms of the scatter? It is essential on such a graph to show the numbers on their original scales, not as logarithms. The scatter is usually easier to motivate once you mention some of the other factors that affect the outcome. $\endgroup$ – Nick Cox Oct 23 '18 at 22:04

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